Vogan's conjecture for p-adic GL(N)

Abstract

Local Arthur packets of 𝑝-adic groups have geometric analogues, called ABV-packets. This was first proposed by David Vogan in [Vog93] following his joint work in [ABV92] for real groups. This theory was then adapted by [CFM+22] in which they formulated the conjecture and named it “Vogan’s conjecture” to honour the work that led to it, in addition to providing a wealth of examples as evidence. In this work, we prove Vogan’s conjecture for 𝑝-adic GL(N).